Problem: Simplify the following expression: $r = \dfrac{54q}{45q - 117}$ You can assume $q \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $54q = (2\cdot3\cdot3\cdot3 \cdot q)$ The denominator can be factored: $45q - 117 = (3\cdot3\cdot5 \cdot q) - (3\cdot3\cdot13)$ The greatest common factor of all the terms is $9$ Factoring out $9$ gives us: $r = \dfrac{(9)(6q)}{(9)(5q - 13)}$ Dividing both the numerator and denominator by $9$ gives: $r = \dfrac{6q}{5q - 13}$